Ancova Homework Help

Analysis of covariance is a general linear model which blends ANOVA as well as regression analysis. It evaluates whether population means of a dependent variable are equal across levels of a categorical independent variable while statistically control the effects of other continuous variables that are not of primary interest which is known as covariate

It can be used to increase statistical power which is the ability to find a statistical significance between groups when one exists by reducing the within-group error variance and then it is necessary to understand the test that is used to evaluate differences between groups and the test is known as F-test where the F-test is computed by dividing the explained variance between groups by the unexplained variance within the groups. If this value is larger than a critical value, then it is concluded that there is a significant difference between groups.

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The variance that is unexplained includes error variance as well as the influence of other factors and therefore, the influence of covariant variable is grouped in the denominator. When the effect of a covariant variable on the dependent variable is to be controlled then it is removed from the denominator making F larger. This will increase the power to find a significant effect if one exists.

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Another use of ANCOVA is to adjust for preexisting differences in nonequivalent groups where this controversial application aims at correcting for initial group differences that exist on dependent variable among several intact groups. In this situation, participants are not made equal by an assignment which is random and covariant variables are used to adjust scores and this will make participants more similar than without the covariant variable.

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However, even with the use of covariates, there are no statistical methods that can equate unequal groups and furthermore, the covariant variable may be so intimately related to the independent variable thereby removing the variance on the dependent variable associated with the covariant variable. This would remove considerable variance on the dependent variable rendering the results meaningless.

The inclusion of a covariate into an ANOVA generally increases statistical power by accounting for some of the variances in the dependent variable. This increase the ratio of variance explained by the independent variables, adding a covariate into ANOVA thereby reducing the degrees of freedom.

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